Definition:Segment of Circle

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Definition

SegmentOfCircle.png

In the words of Euclid:

A segment of a circle is the figure contained by a straight line and a circumference of a circle.

(The Elements: Book $\text{III}$: Definition $6$)


Base

The base of a segment of a circle is the straight line forming one of the boundaries of the seqment.

In the above diagram, $AB$ is the base of the highlighted segment.


Angle of a Segment

In the words of Euclid:

An angle of a segment is that contained by a straight line and a circumference of a circle.

(The Elements: Book $\text{III}$: Definition $7$)

That is, it is the angle the base makes with the circumference where they meet.


It can also be defined as the angle between the base and the tangent to the circle at the end of the base:

AngleOfSegment.png


Angle in a Segment

In the words of Euclid:

An angle in a segment is the angle which, when a point is taken on the circumference of the segment and straight lines are joined from it to the extremities of the straight line which is the base of the segment, is contained by the straight lines so joined.

(The Elements: Book $\text{III}$: Definition $8$)

And, when the straight lines containing the angle cut off a circumference, the angle is said to stand upon that circumference.

(The Elements: Book $\text{III}$: Definition $9$)


AngleInSegment.png

Such a segment is said to admit the angle specified.


Similar Segments

In the words of Euclid:

Similar segments of circles are those which admit equal angles, or in which the angles are equal to one another.

(The Elements: Book $\text{III}$: Definition $11$)


Also see